Hi @Attila Sasvári ,
but when it comes to mobile devices we cannot find a soluton to share the calendar or contacts with different permissions for individual users.
Based on my research and test, I am afraid currently it's not feasible to be realized in Outlook for mobile devices.
As regards to contacts, as far as I know, there's no feature available in Outlook mobile devices to set up sharing permissions or open shared contacts. When it comes to calendars, currently it's only supported to view or edit shared Office 365 or Outlook.com calendars in Outlook mobile devices, see this official blog, so for your scenario that users are hosted on the on-premise exchange server, the guide provided above by mschiavon is not applicable.
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